# How to Find the Fifth Variable with the TVM Solver

The **TVM **(time-value-of-money) **Solver** on the TI-83 Plus graphing calculator can be used to answer questions like What are your monthly mortgage payments? . In fact, if you tell the **TVM Solver** any four of the following five variables, it will figure out the fifth variable for you:

**N:**Total number of payments**%:**Annual interest rate**PV:**Present value**PMT:**Amount of each payment**FV:**Future value

To get the calculator to find these answers, follow these steps:

Set the second line in the Mode menu to 2.

This setting makes the calculator round all numbers to two decimal places, the standard format for money.

Press [APPS][1][1] to select the TVM Solver from the Finance application menu. (On the TI-83, press [2nd][

*x*^{–1}][1].)Enter values for four of the first five variables listed in the TVM Solver. Press [ENTER] after making each entry.

Some values that are entered in the

**TVM Solver**must be entered as negative numbers.This step is illustrated in the first picture.

Don’t worry about any value currently assigned by the calculator to the variable that the

**TVM Solver**is going to find for you. In this example, that variable is**PMT**, the monthly payment.For a loan, the present value is always the amount of the loan; the future value, after the loan is paid off, is (naturally) 0.

You can enter arithmetic problems as values in the

**TVM Solver**. The calculator will do the arithmetic after you press**[ENTER]**. For example, in the first picture,**N**was entered as 30*12.Enter values for P/Y and C/Y. Press [ENTER] after making each entry.

**P/Y**is the number of payments made each year.**C/Y**is the number of times interest is compounded each year.

The calculator assumes these two values are the same. So after you enter the value for

**P/Y**and press**[ENTER]**, the same value is assigned to the variable**C/Y**. (If the values are*not*the same in the scenario for which you’re using the**TVM Solver**, enter the correct value for**C/Y**. As an example, if you’re making monthly payments but the interest rate is a simple interest rate, then**P/Y**= 12 and**C/Y**= 1.)If interest is compounded continuously, it is compounded an infinite number of times a year. But there is no way of entering infinity into the calculator. You can get around this problem by setting

**C/Y**equal to a large number, such as 10^{12}.In the last line, indicate whether payments are made at the beginning or the end of the payment period.

To do so, use

to place the cursor on the appropriate entry, either

**END**or**BEGIN**, and press**[ENTER]**.Place the cursor on the variable for which you want to solve.

This operation is shown in the second picture. In this figure the calculator is told to solve for

**PMT**, the monthly payment.Press [ALPHA][ENTER] to solve for the variable.

The calculator places a square next to the variable it just found. This is illustrated in the third picture.

Press [2nd][MODE] to exit (quit) the TVM Solver and return to the Home screen.